I am implementing game application.In which there is some mosquito(object).They moves randomly on the screen.but i want to move this object like real animation.can u advice me which animation i have to use.And should i have to use cocos2d or quartz core?Please give me advice.
Whether you use Quartz or Cocos2D is up to your own choice. Both are suitable for what you might wish to do. Cocos2D is nice because it has a lot of useful things for developing games already built-in. Quartz is nice because it will have slightly less overhead (though you should not normally notice much effect of the overhead, unless doing some real heavy stuff)
If you want an object to move "randomly" through the screen, you can use a lot of different approaches. For something flying, you can use an angle for direction, and a distance. Then you randomly change distance and direction every time an object reaches its destination.
To make it more realistic you can smooth the animation or make a limit to the amount the angle can change.
Cocos2D has an action object built-in that does this pretty much. You can use MoveTo in combination with an EaseAction. Read up on the Cocos2D documentation to see how to implement that.
Me and my team are working on an iPhone project which uses some flocking algorithms to move objects around using Cocos2D which has held up quite capably. It sounds similar to what you are trying to accomplish. The results are quite fluid. I would highly recommend it.